Mean Free Path Calculator
Free calculate average distance gas molecules travel between collisions. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
Standard atmospheric: 101,325 Pa
N₂: ~364 pm, O₂: ~346 pm, H₂: ~289 pm
Results
Enter parameters to calculate
What is Mean Free Path?
The mean free path (λ) is the average distance a gas molecule travels between collisions with other molecules. It's a fundamental concept in the kinetic theory of gases.
At higher pressures, molecules are closer together and collide more frequently, so the mean free path is shorter. At lower pressures (or higher temperatures), molecules travel farther between collisions.
Mean free path is crucial in understanding gas behavior, diffusion, thermal conductivity, and viscosity. It's also important in vacuum technology - when mean free path exceeds container dimensions, collisions with walls dominate over intermolecular collisions.
Mean Free Path Formula
Where:
- • λ = Mean free path (m)
- • k_B = Boltzmann constant = 1.381×10⁻²³ J/K
- • T = Temperature (K)
- • d = Effective molecule diameter (m)
- • p = Pressure (Pa)
Note: This formula assumes ideal gas behavior and treats molecules as hard spheres.
How to Calculate
-
1
Convert all units to SI
Temperature to Kelvin, pressure to Pascals, diameter to meters.
-
2
Calculate d²
Square the molecule diameter: d².
-
3
Calculate numerator
k_B × T. Multiply Boltzmann constant by temperature.
-
4
Calculate denominator
√2 × π × d² × p. Multiply constants, squared diameter, and pressure.
-
5
Calculate mean free path
λ = (k_B T) / (√2 π d² p). Divide numerator by denominator.
Practical Examples
Example 1: Nitrogen at STP
T = 298 K, p = 101,325 Pa, d = 364 pm (N₂ molecule).
Solution:
λ = (1.381×10⁻²³ × 298) / (√2 × π × (3.64×10⁻¹⁰)² × 101325)
λ ≈ 68 nm
Example 2: Low Pressure
T = 300 K, p = 1 Pa, d = 364 pm.
Solution:
At low pressure, mean free path increases significantly.
λ ≈ 6.9 mm (much longer!)
Applications
Vacuum Technology
Understanding gas behavior in vacuum systems. When λ > container size, molecular flow dominates.
Gas Transport
Analyzing diffusion, thermal conductivity, and viscosity. These properties depend on mean free path.
Atmospheric Science
Understanding molecular collisions in the atmosphere, air quality, and gas mixing processes.
Education
Teaching kinetic theory of gases, understanding molecular behavior, and demonstrating statistical mechanics.
Frequently Asked Questions
How does pressure affect mean free path?
Mean free path is inversely proportional to pressure: λ ∝ 1/p. Higher pressure means more molecules per volume, so more collisions and shorter mean free path. Lower pressure (vacuum) means longer mean free path.
Why does temperature increase mean free path?
At higher temperature, molecules move faster but pressure often increases too (if volume constant). However, if pressure is constant, higher T means lower density, so longer mean free path. The formula shows λ ∝ T/p.
What is the Knudsen number?
Kn = λ/L, where L is a characteristic length (e.g., container size). Kn << 1: continuum flow. Kn >> 1: molecular flow (collisions with walls dominate). Kn ≈ 1: transition regime.
Does molecule size matter?
Yes! Larger molecules (larger d) have shorter mean free paths because they present larger collision targets. The mean free path is inversely proportional to d².
What about mixtures of gases?
For gas mixtures, use an average effective diameter. The mean free path depends on the collision cross-section, which varies with the types of molecules present and their relative concentrations.